@article{10.7287/peerj.preprints.27434v1,
title = {A local search algorithm for the constrained max cut problem on hypergraphs.},
author = {Samei, Nasim and Solis-Oba, Roberto},
year = 2018,
month = dec,
keywords = {Approximation Algorithms, Max k-cut problem, Local Search, Hypergraph},
abstract = {
In the constrained max \textit{k}-cut problem on hypergraphs, we are given a weighted hypergraph\textit{ H=(V, E)}, an integer \textit{k} and a set \textit{c} of constraints. The goal is to divide the set \textit{V} of vertices into \textit{k} disjoint partitions in such a way that the sum of the weights of the hyperedges having at least two endpoints in different partitions is maximized and the partitions satisfy all the constraints in \textit{c}. In this paper we present a local search algorithm for the constrained max \textit{k}-cut problem on hypergraphs and show that it has approximation ratio \textit{1-1/k} for a variety of constraints \textit{c}, such as for the constraints defining the max Steiner \textit{k}-cut problem, the max multiway cut problem and the max \textit{k}-cut problem. We also show that our local search algorithm can be used on the max \textit{k}-cut problem with given sizes of parts and on the capacitated max \textit{k}-cut problem, and has approximation ratio \textit{1-|V\textsubscript{max}|/|V|}, where \textit{|V\textsubscript{max}|} is the cardinality of the biggest partition. In addition, we present a local search algorithm for the directed max \textit{k}-cut problem that has approximation ratio (k-1)/(3k-2).
},
volume = 6,
pages = {e27434v1},
journal = {PeerJ Preprints},
issn = {2167-9843},
url = {https://doi.org/10.7287/peerj.preprints.27434v1},
doi = {10.7287/peerj.preprints.27434v1}
}